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Two Analytical Techniques for Fractional Differential Equations with Harmonic Terms via the Riemann–Liouville Definition

Author

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  • Ragwa S. E. Alatwi

    (Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Abdulrahman F. Aljohani

    (Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Abdelhalim Ebaid

    (Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Hind K. Al-Jeaid

    (Department of Mathematical Sciences, Umm Al-Qura University, Makkah 715, Saudi Arabia)

Abstract

This paper considers a class of non-homogeneous fractional systems with harmonic terms by means of the Riemann–Liouville definition. Two different approaches are applied to obtain the dual solution of the studied class. The first approach uses the Laplace transform (LT) and the solution is given in terms of the Mittag-Leffler functions. The second approach avoids the LT and expresses the solution in terms of exponential and periodic functions which is analytic in the whole domain. The current methods determine the solution directly and efficiently. The results are applicable for other problems of higher order.

Suggested Citation

  • Ragwa S. E. Alatwi & Abdulrahman F. Aljohani & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2022. "Two Analytical Techniques for Fractional Differential Equations with Harmonic Terms via the Riemann–Liouville Definition," Mathematics, MDPI, vol. 10(23), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4564-:d:991176
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    References listed on IDEAS

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    1. Agarwal, Praveen & Singh, Ram, 2020. "Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    2. Alderremy, A.A. & Saad, Khaled M. & Agarwal, Praveen & Aly, Shaban & Jain, Shilpi, 2020. "Certain new models of the multi space-fractional Gardner equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. El Mehdi Lotfi & Houssine Zine & Delfim F. M. Torres & Noura Yousfi, 2022. "The Power Fractional Calculus: First Definitions and Properties with Applications to Power Fractional Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-10, October.
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    Cited by:

    1. Melike Kaplan & Rubayyi T. Alqahtani, 2023. "Exploration of New Solitons for the Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model," Mathematics, MDPI, vol. 11(11), pages 1-9, June.

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